Efficient time-domain model of the graphene dielectric function

A honey-comb monolayer lattice of carbon atoms, graphene, is not only ultra-thin, ultra-light, flexible and strong, but also highly conductive when doped and exhibits strong interaction with electromagnetic radiation in the spectral range from microwaves to the ultraviolet. Moreover, this interaction can be effectively controlled electrically. High flexibility and conductivity makes graphene an attractive material for numerous photonic applications requiring transparent conducting electrodes: touchscreens, liquid crystal displays, organic photovoltaic cells, and organic light-emitting diodes. Meanwhile, its tunability makes it desirable for optical modulators, tunable filters and polarizers. This paper deals with the basics of the time-domain modeling of the graphene dielectric function under a random-phase approximation. We focus at applicability of Pade approximants to the interband dielectric function (IDF) of single layer graphene. Our study is centered on the development of a two-critical points approximation (2CPA) of the IDF within a single-electron framework with negligible carrier scattering and a realistic range of chemical potential at room temperature. This development is successfully validated by comparing reflection and transmission spectra computed by a numerical method in time-domain versus semi-analytical calculations in frequency domain. Finally, we sum up our results - (1) high-quality approximation, (2) tunability, and (3) second-order accurate numerical FDTD implementation of the 2CPA of IDF demonstrated across the desired range of the chemical potential to temperature ratios (4 - 23). Finally, we put forward future directions for time-domain modeling of optical response of graphene with wide range of tunable and fabrication-dependent parameters, including other broadening factors and variations of temperature and chemical potentials.